{
 "metadata": {
  "name": "Motion"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Motion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The motion module allows to define \"motion laws\", functions of time which return (position, velocity, acceleration, jerk) tuples\n",
      "\n",
      "it is inspired from the \"UtlCam\" Delphi unit used in BOBST's CUBE [documented here](http://osterone.bobstgroup.com/wiki/index.php?title=UtlCam)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "sys.path.append(\"D:\\Users\\guglie0p\\Dropbox\\Develop\\Python\\Goulib\")\n",
      "from Goulib.motion import *\n",
      "\n",
      "def plot(pva,t0=None,t1=None,ylim=None):\n",
      "    \"\"\"plots a Segment on pylab\"\"\"\n",
      "    if t0 is None: t0=pva.t0\n",
      "    if t1 is None: t1=pva.t1\n",
      "    x = np.arange(t0,t1, (t1-t0)/100.);\n",
      "    y = [pva(t) for t in x]\n",
      "    y=map(list, zip(*y)) #transpose because of \n",
      "    labels=['Pos','Vel','Acc','Jrk']\n",
      "    for y_arr, label in zip(y, labels):\n",
      "        pylab.plot(x, y_arr, label=label)\n",
      "    pylab.legend()\n",
      "    if ylim: pylab.ylim(ylim)\n",
      "    pylab.show() "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Segments"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Polynomial Segments"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Polynomials are very handy to define Segments as coefficients can easily be determined from start/end conditions.\n",
      "Also, polynomials can easily be integrated or derivated in order to obtain position, velocity, or acceleration laws from each other.\n",
      "\n",
      "Motion defines several handy functions that return SegmentPoly matching common situations"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Segment2ndDegree"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "seg=Segment2ndDegree(0,1,(-1,1,2)) # time interval and initial position\n",
      "plot(seg)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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WC09PT7z//vvw8PDA9OnTa/2D8MknnyAwMBD5+fmK1MgrfjIJTnFMJKhUKhQWFqK4uLhq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\nIrIzDH4iIjvD4CcisjMMfiIiO/P/L922mPMwLqUAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Segment4thDegree"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "seg=Segment4thDegree(0,None,(-2,1),(2,3))\n",
      "plot(seg,ylim=[-2,4])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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m5SZecP/VjRvAxo3AunW0IGTqVGDaNFrVqebxafLZqExL3b1LO2X98gtN1URE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\nLQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "seg=Segment4thDegree(0,2,(-2,1),(None,3))\n",
      "plot(seg,ylim=[-2,4])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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m5SZecP/VjRvAxo3AunW0IGTqVGDaNFrVqebxafLZqExL3b1LO2X98gtN1URE\nADNm0DoJBRY7yWT0JuhHHwGvvAL83//p3po5UadfcnNzERER8dhQj82MhUyQQSbIUN9Qj3pZPeoa\n6lArrcVd6V3USGtQXV+NyrrKpquitgIVNRW4XXsbN2tu4sbdGzAyMELnDp3RtUNXdOnQBV1Nu8LG\nzAY2pjboZtYN9ub2sDO3g31He5i3MdeM0H6UhgZa8PHzz9RPHhYGzJwJhIaKvnSb59qZypSWUvW+\ndi0tdpo1iy5X11bdTEYGLSJqDPaePVUyWtFpdKh7RtOWrwYwgE1PG9j3toeJoQnam7RHO+N2aGfc\nDqYmpjA1MYVZGzOYtjGFRVsLWLSzQMe2HWHV3gqW7SzR3kTL95LOzwfWrKEw79qV+qymTKEj0TQM\nV+1Mpc6coZ+F9etpi4K//Y26uJ6wZr+mBvj8c+D774GYGKrQdWlng8TERCQmJjb9OyYmRnNDXRPf\nKFWbhgZawLFyJW2wNGUKHani5yf2yJ6K59qZytXW0rucq1bRSqGZM4GXX36oPTIxkT7csycd/Gxv\nL85w1UmjK3W9DPWSEnqirlpFz8BXXqEjyDt0EHtkrcZVO1OLy5dpPmXNGtqY5dVXUf5MFN77wBj7\n99M5oVFRYg9SfeTNTh365UUDCALtQz51Ku1fXVAAxMVRe+LMmVoZ6ADgY2qK1IAAjLS0RN+0NKws\nKtLPF2qmWm5u1I8okUCYPQfXPlyGWjsXRGctRGbiNb0KdEUoHOpTpkzB4MGDkZOTA0dHR6xZs0YZ\n49IutbX05k/fvvTGT2AgnT35ww905JgOMDYwwPtOTkj288PPxcUIPXsWeTU1Yg+L6aCcvLYY+fNU\njDFNwc1f4jG2Zz7M+nlR10xamtjD03h6u/hIKUpLge++o/lyPz/gzTepk0WX3r15BO6QYapQW0s7\nKX7zDbUovvFGs2awGzdov9xvvwUcHYF33qE3VrVhu0U58YpSdcrIAP7zH1o5N3ky7eXp7S32qNSO\n59qZshw6RIdWeHlRqDs+7iwYqZQWNP33v3Twx9tvA7NnA+bmah2vOvCcuqoJAh0qMHYsLZxwcaED\nmVeu1MtABx6ca++XloYfeK6dtVJpKS02nT0b+PJLyuvHBjpApfuECbRD6YYNtDWBqyttlF5SorZx\nazIO9aeRyYBt2+gQw8Ze2qtXgX/9C+jSRezRia5xrj3Jzw+rea6dtZBMRm859exJW8NcuABERrby\nRgYOBDZ9GGdtAAAWaUlEQVRtAk6coGMafXxoVdLFiyoZs7bg6ZfHqa+nhRGLF9Ovdu+/T/1UOjyH\npyiea2ctkZ4OvPoq/Sh9/70Sj5UrK6O5m+++o0NiPvhAK9aDPA7PqStLTQ2t+Fy8mBZAfPABPUE4\nnFqsca7d3MgIq728eOdHBoCK6Y8/pp0CPv+cplxU0lNw5w71u//nPxTq//oXHa6uZXhOXVHV1XSQ\noZsbrQD9/Xc6DGDECA70Vmqcax9lZYX+3Neu9wSB9qzz9qa8vXCBjphTWZOYuTkwbx4tZho3jrb/\nHTmSNhTTA1ypV1fT5N6XX9Ic3UcfAQEBYo9KZ3CHjH7LygJefx24fp2mWgYPFmEQdXXAr78Cn31G\nJzV98gkd+ajhuFJvrbt3qS3KzQ1ISaFDdmNjOdCVjDtk9FNVFc1cDhlCxXJamkiBDtB5vXPm0CvM\njBn095AQ+rnXQfoX6nV19EaKhwe1KO7ZQ90tWvyGiqZ7VIdMLnfI6CRBoB8nHx/alPTsWWolF3lH\naWJiQiu+G8N9xgxg9GjqntEh+jP90tBAv4ItWEArHP79b6B/f7FHpXe4Q0Z35eTQomqJhDbfCgkR\ne0RPUVdHTRGffUa/oX/2mUZtzs7TL48jCDSt0rs3LTNet46qcw50URgbGGD+var95+JijDxzhqt2\nLVdVRcv6Bw+mc15On9aCQAdoWuaVV6ivfdgwaoqYPh24ckXskSlEt0M9OZlamWJigCVL6N9Dhog9\nKgbukNEFgkDnont7A7m5dO7FvHk0y6FV2rUD3n2Xwt3dHRgwgLb+uH5d7JHJRTenX86fp8VCFy4A\nCxfSwRQ6vsmWNuMOGe2TkUFTLaWlNNWiSwc+o7SUcmP9egr3efMAU1O1D4OnXwA6WvzFF2mx0MiR\n9IbICy9woGu4xqo99F6HDFftmquigjZIHDaMlvWfOqVjgQ4A1tZ0vNKJE0BmJtCjB7B6Nb0vpwV0\nI+2qqugN0F69ACsresfm7befeN4h0yx/nWvnPWQ0i0xGBxJ5ewOVlfcrdY3oalEVNzda/hobS+cl\n+PkBf/wh9qieSrunX2Qy6mj58EOaK1+0iHZPZFqNO2Q0y7Fj9wN8+XKgXz+xRyQCQaAtJP/5T6rc\nv/pK5buz6t/eL6mpNN9lZESLiLRwbwf2ZDzXLq6iIlpAdOAAHV7BM5mgNsgVK6iAnDKFZgisrFRy\nV/ozp15QQM+uyZNpiiU1lQNdR/FqVHHU1FBm9e4N2NnRW1PTp3OgA6A2yHffpbl2qZSq9e++o79r\nCO3531RTQ4sD+vQBunfnN0H1RONq1ETer13lGpd0+PrSe4THj1O46+ChQorr0oXC/MABYMsWWryU\nmCj2qABoy/RLfDxNtfTuDSxdSiedML0jFQR8dW+ufSHPtSvVmTP0i+/167RZ6ciRYo9IiwgCHW05\nbx6twFqyBHBwUPhmdXP65coVICKCft359lvaVIIDXW81Vu3J3CGjNNeu0WFBo0YBEyfSalAO9FYy\nMKAj9jIzafGSnx/t+lpXJ8pwNDPUa2pob5YBA4CgIODcOdp4hzE83NfOc+2tV1ND58D4+gJmZjSb\n+dprOt6iqGodOgCffkrzVklJFO4iTMlo3vTLvn3A3/9OPefLlgFOTqobHNN63CHTOo1L++fPp9nM\nr76iDUuZkjW2QL79NvDMMzRtbGPTqpvQ/umXkhJqEXr5ZQrzbds40NlTcdXecseP0y++ixbR5oRx\ncRzoKmNgADz7LK3ScnCgInXlSlpbo+q7Fr1Sl8noPMGPPqIl/h99RL/GMNZKXLU/2tWr1G+ekkIN\nZNOn8/npanfuHO0I2Zh3vXo99Vu0s1K/cIFWgq5bByQkUAnBgc7kxH3tD7p1C3jvPVoB6uNDu2fM\nmsWBLopevehVdfZs2uL3ww/p9DUVECfUa2vpWPHgYGDaNODwYY3anJ5pL+5rp6aLZctoNfutW7Rp\n6ccfi7LRIGvO0JBajc6coUOxe/cGDh1S/t0o/RafJjUV8PenX0dOnwZefZUXEDGl89XDql0QgE2b\naJHj/v2UF6tWAba2Yo+MPcDWFvj9d9reZNYs4G9/o1dfJVE4Tffu3QsvLy94eHhg8eLFj//Cykpa\nQDRhArUrbtsG2NsreveMPZY+nY2amAgEBlKb4qpVtF6Pf/nVcOPG0a9RJibUW7p9u3JuV1CAVCoV\n3NzchKtXrwp1dXVCnz59hIyMjAe+BoAgHDggCC4ugjBjhiCUlytyl4zJpV4mExbl5QldDh8WVhYW\nCjKZTOwhKcW5c4Iwdiz9eG3YIAgNDWKPiMklKUkQ5s4VhGbPS3njWaHul6NHjyImJgZ79+4FAHzx\nxRcAgPfff7/pawwMDCA4OgI//ACMGaPQCxBjimreIfOTpydctLRDJj+f5sn37KHOlldf5eMDdI28\n3S8KrR8rLCyEo6Nj078dHBxw/Pjxh75uwQsvUJPs8eMIDg5GcHCwInfLmNwaO2SWSiTol5amdXvI\nlJVRk9j//kcrQHNyAAsLsUfFlCExMRGJSliBqlCot/QHYcGiRYrcDWNK1XjKUkTnzpiVlYXNpaVY\n7eWl0VV7ZSV1tCxbRrtOnz/Pb4Dqmr8WvDExMXLdjkJvlNrb20MikTT9WyKRwEEJu5Mxpg6NVfso\nKyv0v3c2qkzDOmRqa+m0IQ8PWtZx7BjtbceBzh5HoTl1qVQKT09PHDx4EHZ2dhgwYAB+++03eDc7\n5kmlx9kxpiQZVVWYnZUFcw1ZjSqVAr/8cv/o3cajBJj+EGVFqbGxMVasWIHRo0fDx8cHkydPfiDQ\nGdMWPqamONJsD5mVIvW1y2TUa96zJ82bb9gA7NrFgc5aTvy9XxjTMGLsISMI1Fv+r39R2/JnnwGh\nobQvFNNP+nfwNGMqJBUELL13ytKnKuyQEQRa/fnxx0BVFW3HHRXFYc441BlTicaq3dzISOkdMomJ\ntCnp9etATAydPMQ7ZrBG2rlLI2MaThUdMocPA8OH007TL71E7YmTJ3OgM+XgSp2xFmrskDGTs2o/\nfJi6Wa5coemWadP4+Dj2eFypM6ZijR0yzav2lvzQpaTQYc4zZgBTpwLZ2bQ5Hwc6UwWu1BmTQ0s6\nZBITaa48L4/ORJg5kzpbGGsJrtQZU6PHnY3a2M0ydChtkz1zJlXmL77Igc7Ugyt1xhTUWLXX3TKG\nwVeeqMlthw8/pHPUeYqFyUuUXRoZ03cyGZCxxxT1XwTg2hAJqt5Lw+Ierphmrz07PzLdwpU6Y3Ko\nrwd++422we3YkVaCjhsHZFarfzUq0028+IgxNbh7F1i9GvjqK6B7d3oDdMSIB1eASgUBX0kkWCqR\nYKGrK17Sov3amebgUGdMhW7dAr77jrbBHTiQThsKDHzy91y419eu7acsMXFw9wtjKlBUBPzzn4Cb\nG3WxHDxI5wM/LdABwPdeh8xIS0v0b9Yhw5gqcaXO2CNkZNAUy/btwPTpwLx5gJOTArcnws6PTLtx\npc6YggQBSE4GIiOBkBDA1RW4eBH4+mvFAh14uK9drP3ame7jSp3pPakUiI0FliyhufN582hJf/v2\nqrk/rtpZS/AbpYy10p071Mny9deAvT3wj39Qla6O3RK5Q4Y9DYc6Yy2Ulwd88w2wZg1ttDVvHjBg\ngDhjaV61c4cMa47n1Bl7AkEAUlOBSZOAgAD6d1oa8Pvv4gU68OBcu7L2a2f6jSt1ptPq6oDNm4Fl\ny4AbN4A33wTmzAHMzcUe2cMa92s357l2Bp5+YewB164BP/wArFwJeHsDb70FjB0LGBmJPbInU9fZ\nqEzzcagzBuDECZov37WLjoh7/XWgZ0+xR9V63CHDeE6d6a2aGmDtWqB/f+D554E+fejIuJUrtTPQ\nAe5rZ/LjSp1prcbgXrOG3vx84w1gzBjNn2Jprcaq3VzOs1GZduJKnemFhgZg504gPJy6VmQy6mr5\n4w/a+lbXAh24X7W39mxUpp+4UmdaobgY+Pln4McfARsb4JVXaKpFVas+NRVX7fqDK3Wmc2QyqsCj\nowEfH1o0FBsLHD8OzJ6tf4EOcNXOno4rdaZxioponnz1aqBTJ+Dll4GpUzWzt1xMjX3tZly16yS1\nV+qbN2+Gr68vjIyMcOrUKXlvhjEAtKnWzp1AVBR1rOTn06KhU6co1DnQH+ZjaoojXLWzv5C7Us/K\nyoKhoSFefvllLF26FAEBAY++A67U2RNcukRz5f/7H+DiAsydS/3lZmZij0y78GpU3aP2St3Lyws9\nevSQ99uZHquspBAfOhQICgJqa4EDB6iLZe5cDnR5NFbtjX3tfMqS/jIWewBMPwgCkJJCc+WxscCQ\nIcA779DS/TZtxB6dbjA2MMB8JydEdO6MWVlZ2Hz9OlfteuiJoR4aGoqSkpKHPv75558jIiKixXey\nYMGCpr8HBwcjODi4xd/LtNuVK8AvvwDr1lG3yqxZwKJF1JbIVKOxQ+YriQT90tJ4v3YtkZiYiMTE\nRIVvR+Hul5CQEJ5TZw+4dQvYsoWCPCuL+slnzAD69gU4V9Trwr25dt5DRvuI2qfOoc3q6oAdO4CJ\nEwFnZ2DvXjp8oqAAWL4c6NePA10MvryHjN6Ru1KPjY3Fm2++ibKyMlhYWMDf3x979ux5+A64UtdZ\njUv0f/2VKnNvb2DaNDqIwtJS7NGxv+KdH7ULb73L1EIQgLNngQ0bgI0bqX/8hReAKVOoJZFpNt6v\nXXtwqDOVysmhEN+4EaiuphCfOhXo1UvskTF5cNWu+TjUmdJdvQps2kTneBYX07TK888DAwfy/Lgu\nkAoCvpJIsFQi4Q4ZDcShzpQiN5fmxzdtolCPjqYwHzZMN7e1Zdwho6k41JncrlwBtm6lML9yBRg/\nnrpYhg8HjHl5ml5orNq/ule181y7+DjUWatkZ1OQb91KbYfjxwMTJgDBwYCJidijY2LhuXbNwaHO\nnkgQgPR0WqK/bRstEHr2WQryIUN4aoXd17xDhufaxcOhzh4ildJ+K9u309WmDVXk0dF0FJwhH5HC\nnoCrdnFxqDMAtAPiH38AcXHA7t3UOx4VRVW5ry93rbDW4apdPBzqeqygANi1i5bpHz5MLYdRUUBk\nJODoKPbomC5oXrX/5OnJpyypAYe6HpHJgJMnKch37qRTgsaMoSAfPRro2FHsETJdxKtR1YtDXcdV\nVAD79wPx8cCePYCVFTBuHBARAQwaxK2HTH24alcPDnUdIwjA+fMU4Lt301mdQUF0qMTYsYCrq9gj\nZPqMq3bV41DXAbduAQcP0ra1e/dSv/iYMUB4OBASAnToIPYIGXsQV+2qw6GuhRoagLQ0YN8+CvEz\nZ6gaDwujMO/Rg7tVmObjPWRUg0NdS+Tn09z4vn102LKNDTBqFAX50KF05Btj2oj72pWLQ11DVVQA\nSUkU5Pv3A+XlwMiRQGgohbmDg9gjZEx5eK5deTjUNURNDXD0KM2NHzxIb3YOGgSMGEFB7ufHKzmZ\n7mus2s2NjLDay4vn2uXAoS4SqZQ6Uw4dohA/dgzw8aEQHzGC5sj5+cz00V+r9pdsbWHIVXuLcair\niUxGb2gmJNCVkkKrNkeMoK1qhw4FOnUSe5SMaY6Me/u1m/Nce6twqKuITEZnciYm0pWcDFhbU4th\nSAhtVWttLfIgGdNwPNfeehzqSiKVAqdPU3gnJVElbm1NJ/+EhNCftrZij5Ix7cQdMi3HoS6n2lra\nRyU5ma7UVJpOGTqUqvChQ6ntkDGmHFy1twyHegvduUPdKSkpdJ08CXh6UngPGUJX165ij5Ix3cdV\n+5NxqD9GSQltR9t4ZWUBAQH3A3zQIMDCQrThMabXeDXq43Gog97UzM6m8D5yhP4sLwcGD74f4n37\ncoshY5qGq/aH6WWo371L0ydHjtCVmkpVd1AQXc88Qz3jvNiHMc3HVfuD9CLUi4oouBuvc+foiLag\nIKrGg4IAOzul3BVjTCQX7vW163vVrnOhLpVSf3jzEL9zh+bAG0O8f3/ejpYxXcRno4oQ6u+99x52\n7dqFNm3awM3NDWvWrIHFI95xbOnAysqoK6XxOnkScHJ6MMR5K1ogMTERwcHBYg9DJ/BjqVyqeDz1\neb92eUNd7tnmUaNG4cKFCzhz5gx69OiBRYsWtfh7GxqoCl+5Epg5k8LazQ345hs6GGL+fEAiAS5c\nAH76CZg9m9oO9T3QAfrBYcrBj6VyqeLx9DE1RWpAAEItLdE/LQ0ri4o0qkVaE8l9smVoaGjT3wMD\nA7F169bHfm1ZGXD8+P0q/M8/aVVm4zz4P/5Bb2gaGck7GsaYrjI2MMB8JydEdO6MWVlZ2Fxayjs/\nPoFSjiv++eefMWXKlMd+vnt3YMAAmkqZNw8IDAQ6d1bGPTPG9EVj1b5UIkH/tDRejfoYT5xTDw0N\nRUlJyUMf//zzzxEREQEA+Oyzz3Dq1KnHVur8gDPGmHzU3v3yv//9D6tWrcLBgwfRjn8VYowx0ck9\n/bJ3714sWbIESUlJHOiMMaYh5K7UPTw8UFdXBysrKwDAoEGD8N133yl1cIwxxlpH7pbGixcvIi8v\nD+np6UhPT0dkZCS8vLzg4eGBxYsXP/J73nzzTXh4eKBPnz5IT0+Xe9C6bu/evU98LBMTE2FhYQF/\nf3/4+/tj4cKFIoxSO8yZMwfdunVDr169Hvs1/Lxsuac9nvzcbDmJRIKQkBD4+vqiZ8+eWL58+SO/\nrtXPT0EJpFKp4ObmJly9elWoq6sT+vTpI2RkZDzwNfHx8cKYMWMEQRCEY8eOCYGBgcq4a53Tkscy\nISFBiIiIEGmE2iU5OVk4deqU0LNnz0d+np+XrfO0x5Ofmy1XXFwspKenC4IgCHfu3BF69OihlNxU\nylZXJ06cgLu7O1xcXGBiYoLnn38ecXFxD3zNjh07MHPmTADU137r1i1cu3ZNGXevU1ryWALyvSuu\nj4YMGQJLS8vHfp6fl63ztMcT4OdmS9nY2MDPzw8AYGZmBm9vbxQVFT3wNfI8P5US6oWFhXB0dGz6\nt4ODAwoLC5/6NQUFBcq4e53SksfSwMAAqamp6NOnD8LDw5GRkaHuYeoMfl4qFz835ZObm4v09HQE\nBgY+8HF5np9KWXzU0l70v76Ccw/7w1rymAQEBEAikaBDhw7Ys2cPxo8fj5ycHDWMTjfx81J5+LnZ\nepWVlZgwYQK+/vprmJmZPfT51j4/lVKp29vbQyKRNP1bIpHAwcHhiV9TUFAAe3t7Zdy9TmnJY2lu\nbo4O97anHDNmDOrr63Hjxg21jlNX8PNSufi52Tr19fWIjo7GtGnTMH78+Ic+L8/zUymh3q9fP1y8\neBG5ubmoq6vD77//jsjIyAe+JjIyEuvWrQMAHDt2DJ06dUK3bt2Ucfc6pSWP5bVr15pevU+cOAFB\nEJpaS1nr8PNSufi52XKCIGDu3Lnw8fHB22+//civkef5qZTpF2NjY6xYsQKjR49GQ0MD5s6dC29v\nb/zwww8AgJdffhnh4eHYvXs33N3dYWpqijVr1ijjrnVOSx7LLVu24Pvvv4exsTE6dOiAjRs3ijxq\nzTVlyhQkJSWhrKwMjo6OiImJQX19PQB+XsrjaY8nPzdb7siRI/j111/Ru3dv+Pv7A6AtWPLz8wHI\n//xU+SEZjDHG1IdP72SMMR3Coc4YYzqEQ50xxnQIhzpjjOkQDnXGGNMhHOqMMaZD/h8RUk2qAjmr\nLQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}